It is still an open question how equilibrium warming in response to
increasing radiative forcing – the specific equilibrium climate
sensitivity S – depends on background climate. We here present
palaeodata-based evidence on the state dependency of S, by using
CO2 proxy data together with a 3-D
ice-sheet-model-based reconstruction of land ice albedo over the last 5 million years
(Myr). We find that the land ice albedo forcing depends
non-linearly on the background climate, while any non-linearity of
CO2 radiative forcing depends on the CO2 data set
used. This non-linearity has not, so far, been accounted for in similar approaches due to previously more simplistic approximations, in which land ice albedo
radiative forcing was a linear function of sea level
change. The latitudinal dependency of ice-sheet area changes is important for the non-linearity between land ice albedo and
sea level. In our
set-up, in which the radiative forcing of CO2 and of the
land ice albedo (LI) is combined, we find a state dependence in the
calculated specific equilibrium climate sensitivity, S[CO2,LI], for most of the Pleistocene (last
2.1 Myr). During Pleistocene intermediate glaciated climates
and interglacial periods, S[CO2,LI] is on average
~ 45 % larger than during Pleistocene full glacial
conditions. In the Pliocene part of our analysis
(2.6–5 Myr BP) the CO2 data uncertainties prevent
a well-supported calculation for S[CO2,LI], but
our analysis suggests that during times without a large land ice area
in the Northern Hemisphere (e.g. before 2.82 Myr BP), the
specific equilibrium climate sensitivity, S[CO2,LI],
was smaller than during interglacials of the Pleistocene. We thus find
support for a previously proposed state change in the climate system
with the widespread appearance of northern hemispheric ice sheets. This
study points for the first time to a so far overlooked non-linearity
in the land ice albedo radiative forcing, which is important for
similar palaeodata-based approaches to calculate climate
sensitivity. However, the implications of this study for a suggested
warming under CO2 doubling are not yet entirely clear since
the details of necessary corrections for other slow feedbacks are not fully known and the uncertainties that exist in the ice-sheet
simulations and global temperature reconstructions are large.